I think the mathematics associated with quantum mechanics is probably the most difficult--there are plenty of equations that are impossible to solve algebraically (though we can get numerical solutions or approximations for many of them, it just takes a supercomputer or cluster a few days or weeks of chugging...)

Though I think this applies to any complex system. Physics of many interacting bodies or many inter-related processes is bound to come up with some nasty equations.

But what about branches of physics that deal with very poorly understood problems? It seems like it would be pretty hard to study dark matter or dark energy, given how little we know about them...

There are three special things about hydrogen that make it attractive as a fuel:

1) It is very abundant (~10% of ocean's mass and >70% of matter in universe is H by mass)

2) On a "per mass" basis it has unmatched energy density (142 MJ/kg, that's three times that of gasoline or lithium)

3) the only combustion product is water, which is non-corrosive, non-toxic and environmentally benign

There are plenty of reasons that is not an ideal fuel though, for instance: it is relatively expensive to store and transport, forms explosive mixtures with air across a very wide range (18–60% in air can explode, and 4–94% can burn), and easy to ignite.

Anyway, if anybody asks me about the mystery of the missing antimatter, I say what mystery? Then when they say where has all the antimatter gone? I say this:

It hasn't gone anywhere. Weight by weight, you are 99.95% made of it.

ok, then. where has all the matter gone?

This isn't an issue of matter vs antimatter, which, as you have pointed out, is just a matter (no pun intended) of definition. The issue is parity: for each particle that we observe, where is the corresponding antiparticle?

A rocket works, for us laymen, by pushing off something. A terrestrial-launched rocket goes nowhere until thrust is given, pushing the rocket off the pad because the expelled air and heat push off the ground. Or the submarine. When launched from a plane, the rocket is dropped from under the wing, and shortly thereafter its thrust begins and the rocket goes forward, this time because it is pushing on air. Were you to take a Saturn-type setup and drop it from, oh, half a mile up, point upwards, somehow, and let it drop, then fire the thrusters, whether or not you make it up, and so escape that gravitational pull, would be a risky proposition. This is just 1/2 a mile, in Earth atmopshere.

False. A rocket pushes off of itself. By forcing propellent in one direction, the rocket goes the opposite direction. If the rocket were pushing off of something, wouldn't it matter what it was pushing off from? Wouldn't it be more effective to push off the hard, stable ground or launch platform than pushing off the air? Well, it doesn't make a difference what is behind the rocket, so I posit that it isn't actually pushing off.

I think most of the posts on this thread have become so negative in response to the "style of debate" employed by those arguing that thrust cannot work in space. Science is based in evidence--Since we cannot actually show you a rocket working in space without putting you there yourself (though maybe we can crowd-fund to send one of you into orbit...), and any footage we offer is accused of being faked, and any examples of any space missions lead to talk of vast international conspiracies, what evidence are we left with to discuss? Even basic textbook science is "open to debate" because misunderstanding and/or mistrust of well-established theory.

Perhaps one of you would like to put forth some evidence, beyond thought experiment, that rockets don't work in space?

I would like to mention, however, that skepticism is healthy for scientific maintenance and progress. It is good to have people constantly question even those things that we all take for granted. That said, those who question well-established theory are more often wrong than right, and either way, make few friends. Not everyone who questions dogma is a Galileo. I thank you for performing this necessary and usually thankless part of scientific discourse. But in this instance, you're still wrong.

I would think that the higher the charge to mass ratio, the more velocity one could impart on the ions.

Assuming Energy is cheap, and matter to expel is expensive (plus the weight of carrying and accelerating the unused propellant), then one would absolutely want to maximize the velocity the ions are being expelled at.

That's true, but since the speed limit is c for any of these ions, electron to C60–, one should be able to get greater momentum with each particle, the heavier they are. Presumably it would be easier to impart great velocity to the lighter ions than the heavier ones. However, it may be easier to impart greater momentum to the heavier particles, and since it is momentum that is crucial for thrust, perhaps that is the reason heavier ones are used...

Probably, but it would be fairly energy intensive compared to the mass involved. H– is a pretty high energy species, and H2 is non-polar and essentially non-polarizable. It is much easier to ionize HCl because it is pre-polarized and Cl– is much "happier" than H– (for those who object to my personification of ions: H electron affinity is about 73 kJ/mol, vs Cl electron affinity of 349 kJ/mol; given bond dissociation energy of 436 kJ/mol for H2, and 432 kJ/mol for HCl, and 1312 kJ/mol ionization energy of H: H2→ H+ + H– would take at least 1675 kJ/mol and HCl→ H+ + Cl– would take at least 1395 kJ/mol)

I too have wondered why rare heavy ions were the best choice. It shouldn't matter how much each individual ion weighs, if x grams of propellant are ejected from the back of a rocket at a velocity of y m/s, the thrust should be the same.

After thinking about this some more, I think the issue is that one doesn't want the ions to interact with each other--the charge/space density should be fairly small or inefficiencies will arise. Therefore, given a constant thruster size (space and time related by a constant), to have a high mass/second and low charge/space, ions with a high mass/charge ratio would be optimal.

Following this logic, might it not make more sense to use molecular propellants than atomic ones? One can chose a molecule of arbitrary molecular mass, ionization energy, and have some control over the volatility.

Alternatively, a readily ionized substance might be ideal. Sulfuric acid, for instance could be separated into H+ and HSO4– ions. A strong electric field could accelerate the heavy anions backward to generate thrust (and the light cations would go forward).

Another idea would be to use a salt where the anion and cation have (as close as possible) the same mass and charge. For instance the barium salt of dibasic t-butylphosphonic acid (the first such salt I could come up with; the most common isotope of Ba2+ has a mass of 137.91 g/mol, and (CH3)3CPO32– would have a mass of 136.0 g/mol). An electric field (maybe pulsed)would accelerate the ions away from each other, perpendicular to the direction of flight, and a magnetic field perpendicular to both the E field and the direction of flight would be tuned to the right strength to bend the particle paths 90 ° to generate the thrust.

EDIT: H3C-O-CH2-CH2-PO32– would be within 0.2 g/mol of Ba, but isn't as easily made as (CH3)3CPO32–

I think cesium (caesium, Cs) is also used for ion propulsion. It is slightly heavier than Xe (133 g/mol vs 131 g/mol), and althrough it requires more energy to vaporize, it requires significantly less to ionize, overall costing less energy. Wikipedia lists heat of vaporization as 12.64 kJ/mol, and heat of ionization as 1170.4 kJ/mol for Xe; and 63.9 kJ/mol to vaporize Cs, but only 375.7 kJ/mol to ionize it.

The triple bond in N2 is very strong (945 KJ/mol vs O2 with a meager 497 kJ/mol), so it requires a lot of energy to break. Oxygen is also more reactive than expected from its bond dissociation energy because of its unique electronic structure. The most stable form of O2 is paramagnetic, with two unpaired electrons in a half-occupied doubly degenerate orbital, so oxygen can start stealing electrons before its own bond breaks. When excited properly, the two electrons can be forced to pair up, forming singlet oxygen, which is even more reactive.

Easy. Attach the hydrogen to some carbon atoms, burn the whole lot, and plant trees to recycle the resulting CO2 and H2O into more hydrocarbon fuel, using free solar energy.

I agree that it seems the simplest way to store hydrogen is in compounds such as hydrocarbons. It wouldn't make sense to do it in a car, but we have the technology to react hydrogen directly with CO2 to make hydrocarbons (no trees needed--at least as far as C management goes, if all our fuel is made from CO2--of course there are other reasons we need trees). Currently this method is far more expensive than refining what we can dig out of the ground, but I think (hope) this will change in the next 10 years or so as it becomes more expensive to extract fossil fuels (especially if there is an economic mechanism to account for environmental harm) and cheaper to make our own fuels as technology advances and when economies of scale manifest.

A point on HHO generators. These devices are very cheap, but typically convert only 50–65 % of the electrical energy into chemical fuel (the rest is heat waste, and not very useful at that). Additionally, HHO gas (Brown's gas) must be used as it is produced, it's a bad idea to build up any significant quantity of this stoichiometric mixture of hydrogen and oxygen, and store it for any period of time (don't even think of compressing or liquifying it!) If storage is what you're after, an electrolyzer that separates the hydrogen and oxygen is required, and these are significantly pricier.

Zinc-air fuel cells are another option: Have a factory somewhere converting zinc oxide to zinc powder using some source of renewable energy. Fill up your tank with a slurry of said zinc pellets, and convert them into zinc oxide as you drive, then at the fill station the zinc oxide is drained while the zinc is added.

This might not be that feasible, but there are people working on it now. Zinc is fairly heavy, only storing 5.3 MJ/kg (compared to 142 MJ/kg for H2, or 46.4 MJ/kg for gasoline), but it is also very dense so it stores 38 MJ/L (vs 8.5 MJ/L for liquified H2, or 34.2 MJ/L for gasoline). Also if we account for the mass of whatever system is used for storing hydrogen, and the mass difference between combustion engine and fuel cell/electric motor I think the numbers work out even better for zinc.

Wind isn't so much a force as a moving medium. Sailboats take advantage of friction (for both the sail and the keel/centerboard/daggerboard). Can one move upstream in a river (a case where there is a medium driven by gravity) by use of a keel alone? I don't think so...

The a is always there, the v is increasing with t and not constant. Your ballpark is huge.

The orbital velocity decreases with time.

Leave it to the physicists to write a program calculating where the moon was every day of its existence.

Suffice it to say that a few cm a year of receding from Earth isn't enough to fling the moon off towards Jupiter, at least not yet.

No, the Moon's orbital velocity is increasing, not decreasing. The orbital period is increasing. It's somewhat of an oversimplification, but I would say the energy comes mostly from Earth's rotation. We spin about once every 24 hours, while the Moon orbits about once every 27 days--that the tides move are a result of this difference--through the action of the tides (one can think of them as friction) the Earth's rotation is slowing down and the Moon's orbit (velocity) is speeding up.

Without knowing more about the spectrum of the received radio pulse, it is hard to draw many hypotheses. I would agree with JohnDuffield that the extreme power (energy/time) and polarization hint at a natural star-scale phenomenon.

That said, if the spectrum doesn't fit well with any known natural phenomena, especially if it appears very "unnatural" I wouldn't rule aliens out either.

I think this is almost as compelling as the "wow!" signal ( http://en.wikipedia.org/wiki/Wow!_signal )--but with the advantage of having been observed (we think) on several occasions rather than one. Was there anything interesting about the intervals between the six putative radio bursts? (ie regular intervals or monotonic change?) How many are we likely to have missed in the intervening time?

I can see why you wouldn't want to wash your mortar with acid, but I think aqueous ammonia should dissolve copper carbonate (it definitely dissolves Cu(OH)2 and CuO), without reacting with calcium carbonate (marble) or agate.

But if a safe, hard, water soluble salt is what you're really after, I would recommend NaHCO3 or Na3PO4. Unfortunately the really hard salts are also typically insoluble in water (presumably the lattice energy prevents both mechanical breakage and dissolution...)

EDIT: I just looked it up, and malachite is definitely soluble in ammonia. Also a nice bonus with this method is that the copper-ammonia complex is water soluble and very strongly colored, making it both beautiful and easier to see than the starting impurity (even if the mortar looks clean, do another rinse with ammonia--if it turns blue, keep going until it doesn't)

Only insofar as the solar energy keeps our oceans liquid, allowing for much greater tidal displacement.

I think you might be think about tides the wrong way--the Moon isn't dragging the water around the Earth--the Moon and Earth are orbiting each other (on a period of about a month). The two tides are on the side closest to the Moon, where the gravity of the Moon is pulling the ocean slightly more than it's pulling the Earth, and on the farthest side of the Earth, where the Moon is pulling the Earth more than the ocean. The tides are essentially stationary from the Moon's perspective, and the Earth is rotating on its axis such that it looks like the ocean is moving, but really its just the Earth moving (just like the Moon, Sun and stars look like they go around the Earth one a day). Does that make sense?

If I understand this question correctly, it sounds like you want to perform spectroscopy on all points in a line through an object.

The main issue I see here is that the more your EM beam interacts with the subject, the less it will penetrate, and vice versa. This means that you can get a lot of information about the surface of an object, or a little information from deeper in (the depth depending on wavelengths and properties of the subject being analyzed), but there are very few techniques that will allow information to be gathered throughout a macroscopic object.

It is possible to get long range coherent vibrations in well defined crystalline substances, but I would expect it to break down at boundaries within and between objects.

If I have misunderstood your idea, please try to explain it a little more.